Finite Group Databasebeta

← C2×#13073686 #14923837

Subgroups — C2×#13073686 #14923837

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×#66991C211yesmaximal, characteristic, complemented
5#13073686C2116yesmaximal, direct product factor
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66992—28no—
38C2×#66992C2218yescomplemented
39C2×#66991—28no—
40C2×#66991C2218yescomplemented
41C2×#66989—28no—
42C2×#66989C2218yescomplemented
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×C4⋊Dic11C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54C11×#392C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56#10622836C2218yescomplemented
57#10622834C2218yescomplemented
58#10622833C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622574C2218yescomplemented
65#10622569C2218yescomplemented
66#10622564C2218yescomplemented
67#10622558C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69#10622279C2218yescomplemented
70#10622269C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—42no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11—42no—
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C22×D4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11—42no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C23×Dic11—24no—
104C23×Dic11—24no—
105C23×Dic11—42no—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2314yes—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—42no—
117C22×C4×D11C2314yes—
118C22×Dic22—24no—
119C22×Dic22—24no—
120C22×Dic22—42no—
121C22×Dic22C2314yes—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11D418yescomplemented
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144#66992—232no—
145#66991—232no—
146#66989—232no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4D418yescomplemented
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11—42no—
155C2×C4⋊Dic11C2314yes—
156C2×C4⋊Dic11C2314yes—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yes—
159C2×C4×Dic11—24no—
160C2×C4×Dic11—24no—
161C2×C4×Dic11—42no—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66938—232no—
166C11×#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2555—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11C2×D414yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11C2×D414yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C2×D4×C11—28no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—416no—
216C2×D4×C11—416no—
217C2×D4×C11—416no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11C2×D414yes—
228C22×C4×C11#4114yes—
229C22×C4×C11#4114yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—28no—
247C22×Dic11—28no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—44no—
266C22×Dic11—416no—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11C2×D414yes—
270C22×Dic11#4114yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—44no—
281C2×C4×D11—416no—
282C2×Dic22—28no—
283C2×Dic22—28no—
284C2×Dic22—44no—
285C2×Dic22—416no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C22⋊Dic11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11C2×D4116yescomplemented
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4C2×D4116yescomplemented
300C4⋊Dic11—28no—
301C4⋊Dic11—44no—
302Dic11⋊C4—28no—
303C4×Dic11—28no—
304C4×Dic11—28no—
305C4×Dic11—44no—
306C22×#124—111no—
307C22×#124—111no—
308C22×#121—111no—
309C22×#121—111no—
310#2555—1116no—
311C2×#395—111no—
312C2×#394—111no—
313C2×#392—111no—
314C2×#392D1111yescharacteristic, complemented
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×C4×C22⋊C4—111no—
321C2×C4×C22⋊C4—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11C22×D414yes—
364C23×C11C22×D412yes—
365C23×C11C22×D412yes—
366C23×C11C2×#4112yes—
367C23×C11C2×#4112yes—
368C23×C11C2×#4112yes—
369C23×C11H(5,𝔽2)12yes—
370C23×C11H(5,𝔽2)12yes—
371C23×C11C2511yescharacteristic
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11C22×D414yes—
386D4×C11—416no—
387D4×C11—416no—
388D4×C11—416no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
391C2×C4×C11—28no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—44no—
402C2×C4×C11C22×D414yes—
403C2×C4×C11C2×#4114yes—
404C2×C4×C11C2×#4114yes—
405C22⋊D11—416no—
406C22⋊D11—416no—
407C22⋊D11—416no—
408C2×Dic11—28no—
409C2×Dic11—28no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—416no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D414yes—
436C2×Dic11C2×#4114yes—
437C4×D11—416no—
438Dic22—416no—
439C23×Q8—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4C2×D1111yescharacteristic
444C23×D4C2×D1111yescharacteristic
445C23×D4C2×D1111yescharacteristic
446C24×C4—111no—
447C24×C4—111no—
448C2×#124—118no—
449C2×#124—118no—
450C2×#124—228no—
451C2×#124—228no—
452C2×#121—118no—
453C2×#121—118no—
454C2×#121—228no—
455C2×#121—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476#395—118no—
477#394—118no—
478#392—118no—
479#392C2×D1118yescomplemented
480#390—118no—
481#388—118no—
482#388—118no—
483#386—118no—
484#386—118no—
485C4×C22⋊C4—118no—
486C4×C22⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—88no—
516C22×C11—88no—
517C22×C11#53214yes—
518C22×C11#53214yes—
519C22×C11#53814yes—
520C22×C11D4214yes—
521C22×C11#54614yes—
522C22×C11#54614yes—
523C22×C11#55514yes—
524C22×C11C23×D411yescharacteristic
525C22×C11C23×D411yescharacteristic
526C22×C11C22×#4111yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C2×H(5,𝔽2)11yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25C22×D1111yescharacteristic
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×Q8—114no—
555C22×Q8—224no—
556C22×Q8—224no—
557C22×Q8—442no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—24no—
562C22×D4—24no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4—114no—
568C22×D4—114no—
569C22×D4—114no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—442no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4C22×D1114yes—
580C22×D4C22×D1114yes—
581C22×D4C22×D1114yes—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—114no—
590C23×C4—114no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—224no—
595C23×C4—442no—
596C23×C4—442no—
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#124—2232no—
602#124—2232no—
603#121—2232no—
604#121—2232no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—224no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4—442no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—118no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—118no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—114no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—224no—
643C2×C42—224no—
644C2×C42—442no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11—82no—
654C2×C11#255518yescomplemented
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#53211yescharacteristic
657C2×C11C2×#53811yescharacteristic
658C2×C11C2×D4211yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#54611yescharacteristic
661C2×C11C2×#55511yescharacteristic
662D11—44no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—114no—
684C24—112no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24D4×D1114yes—
692C24C23×D1112yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×Q8—228no—
697C2×Q8—228no—
698C2×Q8—444no—
699C2×Q8—4416no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—416no—
710C2×D4—416no—
711C2×D4—416no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—228no—
717C2×D4—228no—
718C2×D4—444no—
719C2×D4—444no—
720C2×D4—444no—
721C2×D4—4416no—
722C2×D4—4416no—
723C2×D4—4416no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—228no—
765C22×C4—444no—
766C22×C4—4416no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4D4×D1114yes—
770C22×C4#434114yes—
771C22×C4#434114yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—444no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—1116no—
783C22⋊C4—1116no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C42—228no—
794C42—228no—
795C42—444no—
796C11C2×#255511yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—114no—
839C23—228no—
840C23—228no—
841C23—228no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1114yes—
853C23C2×D4×D1112yes—
854C23C2×D4×D1112yes—
855C23C2×#434112yes—
856C23C2×#434112yes—
857C23#6703712yes—
858C23#6703712yes—
859C23#41×D1112yes—
860C23C24×D1111yescharacteristic
861Q8—4416no—
862D4—416no—
863D4—416no—
864D4—416no—
865D4—4416no—
866D4—4416no—
867D4—4416no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—44no—
881C2×C4—114no—
882C2×C4—114no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—228no—
886C2×C4—228no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—4416no—
907C2×C4—4416no—
908C2×C4—444no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4C2×D4×D1114yes—
912C2×C4C2×#434114yes—
913C2×C4C2×#434114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—416no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—88no—
937C22—88no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—4416no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22#1062312114yes—
947C22#1062312214yes—
948C22#1062312414yes—
949C22#1062312714yes—
950C22#1062314314yes—
951C22#1062314714yes—
952C22#1062324714yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×#434111yescharacteristic
956C22C22×#434111yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#6703711yescharacteristic
959C22C2×#41×D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—224no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—82no—
974C2—444no—
975C2#1307368618yesdirect product factor
976C2C2×#1062312711yescharacteristic
977C2C2×#1062324711yescharacteristic
978C2C2×#1062312411yescharacteristic
979C2C2×#1062312111yescharacteristic
980C2C2×#1062312211yescharacteristic
981C2C2×#1062314311yescharacteristic
982C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2555
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66938C2semidirect
3. C22×#66992C2semidirect
4. C22×#66991C2semidirect
5. #13073686C2direct (N × H)
6. C2×#10622269C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622569C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#392C2semidirect
38. C2×#66992C22semidirect
40. C2×#66991C22semidirect
42. C2×#66989C22semidirect
53. C2×#66938C22semidirect
54. C11×#392C22semidirect
56. #10622836C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
64. #10622574C22semidirect
65. #10622569C22semidirect
66. #10622564C22semidirect
67. #10622558C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622279C22semidirect
70. #10622269C22semidirect
135. C2×C22⋊Dic11D4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
296. C22⋊Dic11C2×D4semidirect
299. (C2×D11)⋊C4C2×D4semidirect
314. C2×#392D11semidirect
479. #392C2×D11semidirect
654. C2×C11#2555semidirect
796. C11C2×#2555semidirect
975. C2#13073686direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669892
C22×#669382
C22×#669922
C22×#669912
#130736862
C2×#106222692
C2×#106225742
C2×#106228362
C2×#106228342
C2×#106225582
C2×#106225642
C2×#106228332
C2×#106225692
C2×C22⋊C4×Dic112
C2×#106222792
C2×C11×#3922
C2×#255511